6-6 Solving Systems of Linear Inequalities 6-6. Solving Systems of Linear Inequalities
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1 6-6 Solving Systems of Linear Inequalities Warm Up Lesson Presentation Lesson Quiz 1
2 2 pts 3 pts 5 pts Bell Quiz 6-6 Solve each inequality for y. 1. 8x + y < x 2y > Graph the solutions of 4x + 3y > pts possible
3 Questions on 6-5
4 Objective Graph and solve systems of linear inequalities in two variables. COLORED PENCILS
5 Vocabulary system of linear inequalities solution of a system of linear inequalities
6 A system of linear inequalities is a set of two or more linear inequalities containing two or more variables. The solutions of a system of linear inequalities consists of all the ordered pairs that satisfy all the linear inequalities in the system.
7 Example 1A: Identifying Solutions of Systems of Linear Inequalities Tell whether the ordered pair is a solution of the given system. ( 1, 3); y 3x + 1 y < 2x + 2 ( 1, 3) is a solution to the system because it satisfies both inequalities.
8 Example 1B: Identifying Solutions of Systems of Linear Inequalities Tell whether the ordered pair is a solution of the given system. ( 1, 5); y < 2x 1 y x + 3 ( 1, 5) is not a solution to the system because it does not satisfy both inequalities.
9 Remember! An ordered pair must be a solution of all inequalities to be a solution of the system.
10 Check It Out! Example 1a Tell whether the ordered pair is a solution of the given system. (0, 1); y < 3x + 2 y x 1 (0, 1) is a solution to the system because it satisfies both inequalities.
11 Check It Out! Example 1b Tell whether the ordered pair is a solution of the given system. (0, 0); y > x + 1 y > x 1 (0, 0) is not a solution to the system because it does not satisfy both inequalities.
12 To show all the solutions of a system of linear inequalities, graph the solutions of each inequality. The solutions of the system are represented by the overlapping shaded regions. Below are graphs of Examples 1A and 1B on p. 421.
13 Example 2A: Solving a System of Linear Inequalities by Graphing Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. y 3 y > x + 5
14 Example 2B: Solving a System of Linear Inequalities by Graphing Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. Write the first inequality in slopeintercept form. 3x + 2y 2 y < 4x + 3
15 Check It Out! Example 2a Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. y x + 1 y > 2
16 Check It Out! Example 2b Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions. y > x 7 3x + 6y 12
17 In Lesson 6-4, you saw that in systems of linear equations, if the lines are parallel, there are no solutions. With systems of linear inequalities, that is not always true.
18 Example 3A: Graphing Systems with Parallel Boundary Lines Graph the system of linear inequalities. y 2x 4 y > 2x + 5
19 Example 3B: Graphing Systems with Parallel Boundary Lines Graph the system of linear inequalities. y > 3x 2 y < 3x + 6
20 Example 3C: Graphing Systems with Parallel Boundary Lines Graph the system of linear inequalities. y 4x + 6 y 4x 5 The solutions are the same as the solutions of y 4x + 6.
21 Graph the system of linear inequalities. y > x + 1 y x 3 Check It Out! Example 3a This system has no solutions.
22 Graph the system of linear inequalities. y 4x 2 y 4x + 2 Check It Out! Example 3b The solutions are all points between the parallel lines including the solid lines.
23 Graph the system of linear inequalities. y > 2x + 3 y > 2x Check It Out! Example 3c The solutions are the same as the solutions of y > 2x + 3.
24 HOMEWORK Section 6-6 (page 424) 3-13odd, all, 32, 54, 55
25 HOMEWORK
26 HOMEWORK
27 HOMEWORK
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In previous lessons, we have looked at techniques for solving equations, a common theme throughout algebra. In this lesson, we examine some potential dangers where our intuition about algebra may need